OFFSET
1,1
COMMENTS
Although terms k in A277272 are distinct, terms m in this sequence may appear A000607(m) times, even consecutively.
The restriction of the number of appearances of m to A000607(m) is a consequence of distinct k such that A001414(k) = m. Distinct k for which A001414(k) = m relates to the number of prime partitions of m and are listed in row m of A064364. For example, k in {7, 10, 12} have A001414(k) = 7. Once these k have appeared in A277272, there is no other way to obtain m = 7 in this sequence. Hence m = 7 is exhausted in this sequence.
Terms are greater than 1.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10001
Michael De Vlieger, Log log scatterplot of a(n) for n=1..2^17, accentuating n <= 2^10 with small points, and n <= 32 with medium points for better visibility.
MATHEMATICA
m = 2, n = 1, s[_] = c[_] = 0; s[2] = 2; c[2]++; {2}~Join~Reap[Do[k = 3; While[Nand[GCD[If[s[k] == 0, Set[s[k], Total@ Flatten[ConstantArray[#1, #2] & @@@ FactorInteger[k]]], s[k]], s[m]] > 1, c[k] == 0], k++]; Set[n, k]; Sow[s[k]]; c[n]++; m = n, 70]][[-1, -1]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Nov 21 2021
STATUS
approved